Bipolar neutrosophic WINGS for green technology innovation

Green technology innovation is a crucial assurance of achieving sustainable economic and environmental development, so improving the capability of green technology innovation is an urgent problem. In order to provide a more objective and accurate tool for identifying the most important impact factor of green technology innovation, this study innovatively proposes a new method by combining the bipolar neutrosophic sets with Weighted Influence Nonlinear Gauge System (WINGS) method. Furthermore, this paper intends to provide recommendations in improving green technology innovation capability. We invite five experts to evaluate fifteen factors influencing green technology innovation using the bipolar neutrosophic linguistic variables. Then, the proposed bipolar neutrosophic set WINGS (Bipolar NS-WINGS) method is applied to measure the influence of each impact factor of green technology innovation. Finally, we divide all the factors into cause group and effect group. Moreover, the network relation map is constructed to visualize the interrelationships between all impact factors. The Bipolar NS-WINGS suggests that Science and Technology Innovation Environment (Ω7) is the most important factor of green technology innovation. The result also indicates that R&D Investment (Ω8) is the most influential factor in which it has impacted many other factors. It is obvious that the integrated method not only enriches the research in the field of decision theory, which has not combined the bipolar-NS and WINGS method for analyzing relationships of factors, but also contributes to the improvement of green technology innovation capabilities.

In the context of the unstable world economic situation and the prominent ecological and environmental conflicts, green technology innovation has played an important role.Green technology innovation is receiving sustained attention because more and more people are aware of environmental sustainability [1][2][3] .Green innovation not only promotes economic development, but also reduces environmental damage 4 .Green technology is an important part of green innovation that can promote economic and social green development by achieving a balance between environmental protection and economic growth [5][6][7] .To improve green technology innovation capability, we need to figure out the factors affecting green technology innovation.It has been shown that factors such as R&D investment, environmental regulations, etc. influence the capability of green technology innovation [8][9][10] .For example, economic development, environmental legislation and other factors are important driving factors affecting green technology innovation, and industrial scale is the potential driving factor in the construction industry 11,12 .Digital finance can also influence the green technology innovation 13 .Researchers have used different methods to analyze the factors that influence green technology innovation.For example, Yi et al. used the Spatial Durbin Model to analyze the impact of Chinese-style fiscal decentralization on green technology innovation 14 .Li et al. utilized the data of China's A-share listed enterprises from 2010 to 2020 to estimate the influence of government environmental punishment on green technology innovation based on the fixed-effect model 15 .And Hu et al. used the difference-in-differences model to analyze the impact of ecological civilization construction on green technology innovation 16 .
It can be seen that there are many factors that affect green technology innovation, so which is the most important one?Are there any correlations among the factors?These questions need to be addressed urgently.Unfortunately, previous studies are mainly premised on independent factors and ignores the interrelationships between the factors.Therefore, it is necessary to analyze the factors affecting green technology innovation to determine the influence of each factor and thus identify the most critical ones.It is a complex problem to study the interrelationship between the factors because of many uncertain and fuzzy variables.We can deal with this uncertainty problem with the help of fuzzy set theory.For example, Bao analyzed eight elements in the innovative governance system taking the data of agriculture-related enterprises based on the fuzzy-set qualitative comparative analysis (fsQCA) 17 .Dong et al. presented a dynamic intuitionistic fuzzy decision-making method to choose digital green innovation investment projects 18 .

Bipolar neutrosophic set
Similar to the definition of neutrosophic set, the bipolar neutrosophic set (Bipolar NS) is presented in Definition 2. Definition 2 28 A Bipolar NS V in is defined using the following equation: where denote the truth-membership, the indeterminacy-membership and the falsity-membership of an element ψ ∈ � associated to a Bipolar NS.Then, the negative membership degree T − V (ψ), I − V (ψ) and F − V (ψ) denote three memberships of an element ψ ∈ � to some absolute opposed quality associated to a Bipolar NS.In brief, we can use a kind of simple form V = T + , I + , F + , T − , I − , F − to represent an element ψ in a neutrosophic set, and the element ψ is called a bipolar neutrosophic set number.

Arithmetic operations of bipolar NS
The bipolar NS also fulfil some basic arithmetic rules such as inclusion, equality and so on.The rules of Bipolar NS are shown as follows.Definition 3 28 Given two bipolar neutrosophic sets Then, some rules are shown in the following.

Complement
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Bipolar NS-WINGS method
In this section, the Bipolar NS and the WINGS method is integrated to solve specific MCDM problems.It contains three stages as in Fig. 1.Firstly, obtaining the original evaluation matrix.Secondly, the original evaluation matrix will be aggregated.Thirdly, applying the WINGS method to analyze factors.The following steps of the suggested method in detail are displayed.

Obtain the original evaluation matrix
Step 1 Define the bipolar neutrosophic set linguistic variables.
Firstly, we introduce the linguistic variable and they are used to determine the degree of interaction or influence between factors.Then, we propose Bipolar NS linguistic variable based on the Definition 3. It is important that the memberships in bipolar neutrosophic set must meet the requirements where . The linguistic variables and Bipolar NS linguistic variable are presented in Table 1.
Step 2 Select impact factors and collect questionnaires evaluated by experts.Firstly, we determine the impact factors and distribute questionnaires to experts and invite them to evaluate the factors using the five linguistic variables presented in Step 1. Suppose that there are K experts evalu- ating n impact factors.Experts are symbolized by E e = {E 1 , E 2 , ..., E k }(e = 1, 2, ..., k) , and impact factors by � i = {� 1 , � 2 , ..., � n }(i = 1, 2, ..., n) .Then, we collect evaluations of each expert and convert it into bipolar neutrosophic set linguistic variables.Let A k ij be a bipolar neutrosophic decision matrix of the Kth experts, the original matrix is denoted by:

Aggregate the original evaluation matrix
Step 3 Aggregate evaluations of each expert.
Let A ij be an aggregated decision matrix, and it is denoted by: where .., n.Experts' evaluations can be aggregated using the following equation: Step 4 Calculate the crisp number matrix.The crisp number can be obtained by the following de-neutrosophication equation: After that, we can obtain a matrix containing only crisp numbers.Let B ij be a crisp number matrix, then the matrix is denoted as:

Apply the WINGS method
Step 5 Normalize the crisp number matrix and calculate the total relation matrix.
We can normalize the crisp number matrix by the equation: where Then, the total relation matrix can be computed by the following equation: where D denotes the identity matrix and F denotes the total relation matrix.
Step 6 Compute the sums of rows and columns.By simply adding the elements in the rows or columns of matrix F , we can obtain the value of P and Q ,which denote the sum of rows and columns respectively.The equations are defined as: (2) Table 1.Linguistic variable and Bipolar NS linguistic variable.

Linguistic variable Bipolar NS linguistic variable
No influence (NO) < 0. www.nature.com/scientificreports/ Step 7 Build the causal diagram.Firstly, we compute the value of P + Q and P − Q , which are called prominence and relation.The value of P + Q indicates how significant each factor is.The value of P − Q indicates the overall impact of each factor that is added to the system.In addition, P − Q has positive and negative values.The positive value is referred to as net causer while the negative value is called net receiver.Then, we construct the causal diagram by horizontal axis P + Q and vertical axis P − Q.
Step 8 Calculate threshold value and create network relationship map.The threshold value (x) is calculated by averaging the elements in the total relation matrix F 50 .The element is identified as "0" if it is less than x , which indicates that it has less influence than other factors.On the contrary, if it is more than x or equal, the element is identified as "1", which means their influence is higher than the other factors.Next, the network relationship map is drawn to describe the connections between the impact factors in decision-making problems.

Results
In this section, the bipolar NS-WINGS method is applied to analyze the factors of green technology innovation.The specific process and results for aggregation are shown in the following subsection.

Data collection
Step 1 Define the bipolar neutrosophic set linguistic variables.
The first step is introducing the linguistic variables based on the bipolar neutrosophic set.Based on the WINGS method, we define five linguistic variables firstly, then we transform them into bipolar neutrosophic set linguistic variables.Table 1 shows the linguistic variables and bipolar neutrosophic set linguistic variables.
Step 2 Select impact factors and collect questionnaires evaluated by experts.Firstly, we select 15 impact factors of green technology innovation with reference to previous literature 5,9,11,51 .These factors are presented in Table 2.Then, in order to collect data, we distribute questionnaires to five experts and invite them to evaluate the factors that influence green technology innovation.The details of these experts are presented in Table 3. Specifically, the experts score the degree of influence among 15 influencing factors using the five linguistic variables in Table 1.Finally, we convert it into bipolar neutrosophic set linguistic variables.One of the experts' evaluation matrix is shown in Table 4.

Bipolar NS-WINGS analysis
Step 3 Aggregate evaluations of each expert.
Experts' evaluations are collected by using the Eq.(1), Table 5 presents the final results.
Step 4 Calculate the crisp number matrix.Table 6 shows the crisp number that is calculated using the Eq.(2).
Step 5 Normalize the crisp number matrix and calculate the total relation matrix.
We can use the Eq. ( 3) to normalize the crisp number matrix and Table 7 shows the final result.
(5) www.nature.com/scientificreports/ The total relation matrix F can be obtained using the Eq. ( 4).Table 8 shows the final results.
Step 6 Compute the sums of rows and columns.
We can obtain the values of P and Q by summing elements rows or columns of total relation matrix F .Table 9 presents the values of P, Q, P + Q and P − Q .In P column, we can see that Ω 8 has the maximum value of 26.1691, and Ω 12 has the minimum value of 23.5466.For P + Q , Ω 7 is the most significant factor with the largest value, and Ω 12 is the least significant factor because it has the smallest value.By comparing P + Q , we can see the dif- ference in the importance of each impact factor.Then, the ranking of the impact factors is obtained as Ω 7 > Ω 10

Discussion
In this part, the Bipolar NS-WINGS method is contrasted with WINGS method and DEMATEL method to proof the validity and reliability.Table 11 shows the specific comparative results.We can see that the ranking of three methods is similar and it can proof the feasibility of the Bipolar NS-WINGS method.However, there are some differences in the results of these three methods.The WINGS and DEMATEL have the same result, while the cause group of the Bipolar NS-WINGS method has one less factor than the other two methods.The reason for this difference is that the Bipolar-NS WINGS combines the bipolar neutrosophic set, which is beneficial to handle vague and uncertain information.
In contrast to DEMATEL, both Bipolar-NS WINGS and WINGS consider the effect of the factor itself, which is useful for studying the interrelationship between the factors.And compared to WINGS and DEMATEL, the Bipolar-NS WINGS combines the bipolar neutrosophic set, which is beneficial to integrate the opinions of different experts.Therefore, compared with other methods, the method proposed in this paper has the following advantages.Firstly, this method is based on the bipolar neutrosophic set, which can employ linguistic variables to express the expert's tacit knowledge and help make evaluations.The main significance in application of this work is to define and develop an effective evaluation framework to guide managers in assessing the factors affecting the ability to innovate in green technologies.This method overcomes the one-sidedness of DEMATEL and WINGS, and makes the evaluation result more objective and real.In addition, the results of comparison with  www.nature.com/scientificreports/ the other two methods confirm that the final ranking of the method is credible.Obviously, this study provides a more accurate, effective and systematic decision support tool for studying the influencing factors of green innovation capability.Secondly, using the WINGS approach enables consideration of the factors themselves and the interactions between factors.According to the final results, it can classify factors into causal group to identify cause-and-effect relationships between factors.The results show that Technological Innovation Environment (Ω 7 ) is the most important factor and R&D investment (Ω 8 ) is the most influential factor, which has an impact on other factors.Therefore, managers should focus on these two factors.Increasing R&D investment and improving the technological innovation environment play an important role in improving the ability of green technology innovation.Finally, this study can help researchers to better understand the problem of green technology innovation ability in theory, and also help organizations to design and develop a better green technology innovation ability evaluation system.And the novel method can be applied in more environments where information is ambiguous and uncertain, and it has generality.There are some limitations to this article.Firstly, the evaluation of each expert may have some prejudice and more experts may be requested to participate in this evaluation in the future.Secondly, we only considered 15 impact factors that affect green technology innovation, so there may be some other factors that are not considered.Finally, more MCDM methods can be combined with the bipolar neutrosophic set based on this paper in the future.

Conclusions
Green technology innovation is receiving sustained attention because more and more people are aware of environmental sustainability.To improve green technology innovation capability, we need to figure out the factors affecting green technology innovation.Therefore, we propose a novel method combining bipolar neutrosophic set with WINGS method to analyze the interrelationship between factors and rank them by influence.Firstly, we define the bipolar neutrosophic set linguistic variables and select fifteen impact factors of green technology innovation.Secondly, we invite five experts to score the importance of each factor and convert it into bipolar neutrosophic set number matrix.Thirdly, we aggregate the crisp number matrix and calculate the importance of each factor by using the Bipolar NS-WINGS method.In addition, we obtain the relationship between impact factors and the causal groups of green technology innovation by applying the proposed Bipolar-NS WINGS method.This paper also shows the interrelationship between factors by constructing the network relationship map.These findings can provide some initial guidance for improving green technology innovation capabilities, and it is meaningful for studying the relative relationships among the factors affecting green technology innovation.
The final result indicates that the most important factor is Science and Technology Innovation Environment (Ω 7 ).It means that Science and Technology Innovation Environment is the most important factor for improving green technology innovation capabilities.As we all know, Science and Technology Innovation Environment is the basis for innovative activities and creating a good innovation environment is the first step to improve the capabilities of green technology innovation.The support of local governments for scientific and technological innovation can effectively promote the enthusiasm of green technology research and development, guide the implementation of green innovation activities and improve the ability of green innovation.Therefore, policy makers should strive to create a favorable environment for green innovation 52 .For example, the government should continuously optimize the construction of innovation infrastructure and the structure of fiscal science spending and attract more market forces to participate in green technology innovation activities.Environmental Regulations (Ω 10 ) is the second most important factor.In fact, scholars have extensively explored the effects of environmental regulations on the effectiveness of green development of urban industries, etc., and generally found that environmental regulations have the impacts of short-term inhibition and long-term promotion 53,54 .Some studies have shown that the excessive growth of environmental regulation level will inhibit green innovation, so it is necessary to properly control the level of environmental regulation.Different types of environmental regulations may have different impacts on green technology innovation.Therefore, the government should formulate reasonable environmental regulation standards.
Government subsidies (Ω 6 ) is also an important factor.The development of innovation activities requires a large amount of capital investment.General scholars believe that the degree of government support for enterprise innovation activities can make up for the lack of investment in enterprise green technology innovation, and then have a positive effect on enterprise green technology innovation.Therefore, the government should consider increasing research more subsidies to improve green technology innovation capabilities.Foreign investment (Ω 13 ) will intensify local market competition, and then have a certain incentive effect on industrial enterprises, forcing local enterprises to increase research and development investment to improve the level of technology.Economic Development (Ω 14 ) and Level of urbanization (Ω 3 ) are also important factors affecting the ability of green technology innovation.Generally speaking, the higher the level of regional economic development, the greater the protection of the environment and the more urgent the need for green development.The high level of urbanization often indicates a more developed level of local economic development, a more complete urban management system, and a stronger attraction for professional and technical talents, which plays a positive role in promoting local governments and enterprises to carry out green technology innovation activities and improve green technology innovation capabilities.
This study also notes that R&D Investment (Ω 8 ) is the most influential factor in which it has impacted many other factors.R&D investment, as a form of expression of technological level, directly determines the output results of the region.Rational use of R&D funds, precise investment, and clear innovation types can promote the coordinated development of economy and environment and improve the ability of green technology innovation.Therefore, increasing R&D investment will have an impact on other factors, such as improving the R&D environment.Generally speaking, the more invested in R&D, the easier it is to conduct innovative activities,

Figure 1 .
Figure 1.Flow chart of Bipolar NS-WINGS method.

Table 2 .
Impact factors for green technology innovation.

Table 3 .
Information of the experts.

Table 4 .
Evaluation matrix of one of the experts.

Table 9
. P + Q and P − Q for factor.